Method and an article of manufacture for determining optimum operating points for power/cost and helium-air ratios in a tubular transportation system

ABSTRACT

A tubular transportation system is disclosed for transporting one or more passengers or one or more cargos via a capsule along a predetermined route. A method and an algorithm are described for determining optimum operating points for power/cost and helium-air ratios in a plurality of substantially evacuated tubes in a tubular transportation system for transporting one or more passengers or one or more cargos via a capsule along a predetermined route.

RELATED APPLICATIONS

This application is a continuation of U.S. Ser. No. 16/022,696 filedJun. 29, 2018.

BACKGROUND OF THE INVENTION Field of Invention

The present invention relates generally to the field of tubetransportation. More specifically, the present invention is related totube transportation systems using a gaseous mixture of air and helium.

Discussion of Prior Art

The recent effort to develop a high-speed and efficient new mode oftransportation, which Elon Musk termed the Hyperloop, began in 2013 withthe release of his technical white paper. A team of Space-X and Teslascientists wrote this paper to define technical advantages andengineering requirements to build such a device.

Essentially, the Hyperloop is a system where a capsule is levitated in atube at low-pressure (and in turn low air density). Levitation reduces,substantially, ground friction. Low air density reduces, substantially,air drag.

The white paper proposed an air-ski supported capsule riding inside ofan evacuated tube, 100 Pascal (Pa) absolute, and propelled by linearinduction motors. An air compressor was placed at the nose of thecapsule to provide air to the ski pads and to improve the speedcapability of the capsule. The inclusion of a large compressor improvedthe capsule speed but required a large battery array to power it duringthe Hyperloop journey. It additionally took valuable space from thepassenger compartment and added significant complexity. Several groupstook immediate notice of the white paper and began development of thesystem proposed in the white paper.

Some design teams involved in such development moved away from theair-ski concept as it required a ski-to-tube distance of only0.020″-0.040″, which would make it difficult to maintain a smooth ridewhile accommodating tube and installation tolerances. One replacement ofthe air-ski was a Maglev (Magnetic Levitation) based system. Such aMaglev system would remove the need of a compressor, thereby reducingcapsule size/weight, and would provide developers with the addedadvantage of increased space and decreased vibration.

However, removing the compressor in the design made way for anothermajor problem in such tube-based transportation systems. In the originaldesign as outlined in Musk's white paper, the compressor serves as animportant component for improving the speed of the capsule, where suchimprovement is not due to the thrust provided to push the capsule downthe tube but is due to the reduction in the effective frontal area ofthe capsule. In Musk's design, the compressor provided a second path todirect air from in front of the capsule to the rear of capsule, addingto the annular region between the capsule and tube. The ratio of thisannulus to total tube area, known as the bypass ratio, is a keypredictor of choking. Once the capsule reaches a speed where chokingoccurs in the bypass area, the capsule would act as a huge plunger,creating a type of syringe effect. At that key point, known as theKantrowitz limit (or K limit), immense drag due to the long column ofair in front of the capsule being pushed requires significantly moreenergy and power to overcome. Overcoming the choking, or K limit, andachieving a significant reduction in the K limit effects is a keytechnological concern.

A discussion is now presented with regards to the issues associated withdrag and the choked flow phenomenon. FIG. 1 depicts a schematic of avehicle (also referred to as pod or capsule) within a tube (Source: seepaper to Chin et al. titled “Open-Source Conceptual Sizing Models forthe Hyperloop Passenger Pod”, dated 5-9 Jan. 2015).

Drag is mainly the contribution of two components: pressure drag andfriction drag. Pressure drag is the pressure exerted as the vehiclemoves forward and pushes the air. Friction drag is the viscous forceexerted by the air that flows around the vehicle surface. Drag is givenby the equation below:D=C _(D)½ρ_(tube) V _(pod) ² S _(pod)  (EQN. 1)

where:

ρ_(tube)=Pressure in the tube, absolute;

V_(pod) ²=Velocity of the pod squared;

S_(pod)=Surface area of pod; and

where C_(D) is the drag coefficient that includes pressure drag and dragdue to friction effects.

In EQN 1, the drag is proportional to density. Consequently, reducingdensity has a substantial effect on drag and in turn on propulsionpower. This can be obtained with a low-pressure tube. In EQN 1, the dragis proportional to the square of the velocity. Thus, drag rises fastwith increasing velocity.

Reducing density around vehicle is a historical idea that was firstapplied in the field of aeronautics. Aircraft fly at high altitude wherethey experience low density and therefore low drag. In a low-pressuretube, the environment is controlled to reduce the density. However,reducing the pressure is just one of the different options to reducedensity (other options are increasing temperature and using lightgases). Hence, in a low-pressure tube, it is expected that drag will besubstantially reduced due to the much lower density, even at highvelocities (this is true until a certain limit velocity).

An undesired flow phenomenon occurs when the vehicle reaches highsubsonic speed. The air that flows around the vehicle in the bypass gapin FIG. 1 gets choked. This results in a large increase of pressure infront of the vehicle. In turn, drag increases and the requiredpropulsion power becomes greater. A description of the physicalphenomenon of choked flow is now provided where the key physics relatesto the speed of sound.

As the vehicle moves forward, it pushes the air in front which increasesupstream pressure. Since the back of the vehicle is still atlow-pressure, a pressure difference is created. Pressure wavestravelling from the vehicle's back to the vehicle's front communicatesthe downstream pressure state forward, and it informs of the pressuredifference, like a spring. In reaction, the mass of air in front of thevehicle escapes through the bypass gap. As long as enough air escapes tothe back, an equilibrium is created, and the pressures remain relativelylow. Hence, the amount of air flow must compensate for the pressuredifference between the front and the back. Then, an equilibrium exists.This equilibrium mechanism is illustrated in FIG. 2.

However, when the vehicle reaches high speed, the air flow getsaccelerated in the bypass gap and can reach the speed of sound. Hence,the air flow in the bypass becomes as fast as pressure waves in theopposite direction. As a result, pressure waves cannot travel backagainst the air flow and never reach upstream location. Consequently,the information of the pressure state downstream can no longer reachthrough the sonic flow point and communicate the pressure difference tothe front of the capsule. The upstream air is not well informed of thepressure difference and the right amount of air no longer flows towardthe low-pressure region behind the capsule. This choking scenario isdepicted in FIG. 3. A column of air builds up in front of the vehicleand upstream pressure rises. This choking flow is referred to as theKantrowitz limit. The result is that upstream pressure increasessubstantially due the vehicle motion which acts as a large plunger andthe drag increases accordingly. Consequently, the power requirement tomaintain the vehicle speed becomes very high.

FIG. 4 depicts a graph of drag versus vehicle speed which identifies thecritical vehicle speed that demarcates the pressure equilibrium scenariodepicted in FIG. 2 and the choked flow scenario depicted in FIG. 3.

One key physics is therefore to let pressure waves reach the front ofthe vehicle, where the pressure waves must be faster than the air flowin the bypass gap. It should be noted that this phenomenon occurs if thebypass gap is small, because the air flow gets accelerated even more insmall sections. Unfortunately, for engineering application, the vehiclesize is to be maximized to accommodate passengers or cargo. In otherwords, the bypass gap size should be minimized. The question, therefore,is: how fast can a vehicle go with a small bypass size?

Formally, a maximum vehicle speed can be defined at which choking flowoccurs. This maximum speed has been studied in the previously notedpaper to Chin et al. (2015). FIG. 5, extracted from the Chin et al.(2015) article, depicts a graph of the bypass area ratio (Bypass/Tube)versus the bypass air flow Mach number. FIG. 5 demonstrates that, for areasonable vehicle size (bypass area less than 50% of tube area), themaximum vehicle speed is about Mach 0.25. This corresponds to 300 km/h.This is clearly unacceptable for such a novel transportation system.

There are several ways to get around this issue. One solution noted inElon Musk's White Paper is to use an axial compressor at the front ofthe capsule. Such a design is depicted in the previously noted Chin etal. paper, which is reproduced in FIG. 6(A). In the scenario depicted inFIG. 6(A), the compressor forces a portion of air into an internal pathinside the vehicle instead of going only in the bypass gap. The effectis to increase dramatically the net bypass area for the air flow andthereby avoid acceleration and choking phenomenon at low vehicle speed.FIG. 6(B) depicts a drag curve (as noted in the above noted Chin et al.paper) which shows that the maximum vehicle speed is Ma=0.6 beforechoking phenomenon. This corresponds to 600 km/h. While the increase inspeed is interesting, it is still far from higher speeds (such as atarget speed of 1,000 km/h, for example).

The drawback of the approach depicted in FIGS. 6(A)-(B) is that theinstallation of a compressor introduces significant cost, complexity inthe design of the vehicle, and safety issues. Regarding safety,Uncontained Engine Failure (UERF) where the blade of the compressor canbreak and damage the vehicle itself, the tube, and other vehicles, andinduce high constraints in the development of such a transport system.

Another solution is to decrease the tube environment to extremelylow-pressure, as mentioned in the previously mentioned Elon Musk's WhitePaper. It could be expected that at low enough tube pressures, thespacing of the gas molecules would become so distant that they wouldflow around the capsule without choking. In the event there would stillbe a choking effect, the drag increase, and power to push the air columnat this very low air density would be insignificant. At extremelylow-pressure, below 0.1 Pa-1 Pa, the air can no longer be considered asa physical continuum, as in classical fluid dynamics, but must betreated with molecular flow theory. It is expected that in this flowregime, the choking phenomenon does not occur or has less impact. Andeven if it exists, pressure would be so low that drag could beinsignificant.

The drawback with this second solution is that the power requirements,cost and engineering design to maintain extremely low-pressure in such alarge volume can be tremendous. The pump power requirement to maintainvacuum rises in an exponential manner as the target tube pressure goesbelow 100 Pa. It becomes tremendous when going below 1 Pa. However, thelimit between classical fluid dynamics and molecular flow, has not beenclearly demonstrated in such transport systems. Thus, the effort turnedtowards modeling the flow dynamics versus pressure to find the keypressure below which high speeds and low drag could be achieved.

Computational fluid dynamics (CFD) was used to explore this problem. Onedifficulty in CFD modeling is that the low-pressure ranges that neededto be modeled were beyond normal continuum flow mechanics, and thusstandard computer models struggled to give reliable outputs. Worse yet,the level of vacuum (tube pressure) that was required would necessitatevery large vacuum pump systems and consume much energy. Thus, a tradeoffwas made to explore pressure ranges of 1-10 Pascals absolute, which werethought to be low enough to provide a Kantrowitz limit work around, butalso high enough that vacuum pump systems were economical.

Several difficulties with the CFD models became quickly apparent: (1)this pressure range is in a transition flow region between continuum andmolecular flow; since different modeling tools must be used in eachregion it became problematic to get reliable data through that pressureregion, (2) many assumptions needed to be made which had yet to beverified; thus, test apparatus would need to be developed to validatethe computer models, and (3) there are currently no computers availablein the commercial arena with the ultra-high processing capabilityrequired to handle the complexity of a moving capsule inside of a tube.This leads to another untested assumption—whether the validity ofmodeling a fixed capsule with moving air around it, instead of a movingcapsule through still air inside of the tube is accurate. Testing thevalidity of this assumption would again require a test apparatus.

The effort to find the theoretical and economical pressure that allowedhigh speeds and low drag became a focus of various development groups.It was clear that at some pressure the choking phenomena would beinsignificant. This is demonstrated by craft flying in near earth orbitpressures, near and beyond the transition region to molecular flow, thatexperience nearly zero drag. Below this key pressure point and with aparticular tube/capsule geometry there would be the ability to have highvelocity and low drag.

Prior art approaches have suggested using hydrogen to accomplish thisspeed improvement. In such prior art systems, a tube operating atatmospheric pressure (or slightly above) and has at least the followingdisadvantages:

1) The standardized volume of hydrogen (or other small diameter gas)required to fill a 4-meter diameter tube, perhaps 100 to 500 km long, atatmospheric pressure is significantly beyond anything currently built.However, this preferred art operates at 1/1,000 to 1/10,000 of anatmosphere and thus the gas mass required is also 1/1000 to 1/10,000less per kilometer,

2) No method is described suggesting how to replace the air inside thetube with hydrogen, and

3) Although hydrogen is not flammable above 75% concentration, adistinct safety issue occurs in the event of a tube breach which willintroduce air into the tube and has the potential to create flammable orexplosive ratios. A tube breach event must be planned for and can beexpected at some point due to earthquake, damage due to operations oreven sabotage.

Another prior art, German patent publication, DE 2054063 A1, discloses ahigh-speed passenger and container mass transit system using helium.However, the German patent publication, much like the current tube-basedtransportation systems, fails to utilize a mixture of air and helium,where the composition of each gas in the mixture is dynamicallydetermined to optimize drag. Furthermore, the German patent publication,much like the current tube-based transportation systems, fails toutilize a mixture of air and helium, where the composition of each gasis dynamically determined depending on the desired velocity of thecapsule.

Whatever the precise merits, features, and advantages of the above citedreferences and above noted prior art systems, none of them achieves orfulfills the purposes of the present invention.

SUMMARY OF THE INVENTION

In one embodiment, the present invention provides an article ofmanufacture having non-transitory computer readable storage mediumcomprising computer readable program code executable by a processor toimplement a method to determine optimum operating points for power/costand helium-air ratios in a plurality of substantially evacuated tubes ina tubular transportation system for transporting one or more passengersor one or more cargos via a capsule along a predetermined route, thenon-transitory computer readable storage medium comprising: (a) computerreadable program code identifying a speed of the capsule; and (b)computer readable program code identifying a pressure to be maintainedwithin a tube amongst the plurality of substantially evacuated tubes;and (c) computer readable program code identifying, for the speedidentified in (a), a helium-air ratio based on an analysis of a totalpower required at a plurality of percentages of helium for the pressureidentified in (b); (d) computer readable program code sendinginstructions to maintain within the tube amongst the plurality ofsubstantially evacuated tubes, a percentage of helium according to thehelium-air ratio identified in (c).

In another embodiment, the present invention provides an article ofmanufacture having non-transitory computer readable storage mediumcomprising computer readable program code executable by a processor toimplement a method to determine optimum operating points for power/costand helium-air ratios in a plurality of substantially evacuated tubes ina tubular transportation system for transporting one or more passengersor one or more cargos via a capsule along a predetermined route, thenon-transitory computer readable storage medium comprising: (a) computerreadable program code identifying a speed of the capsule; (b) computerreadable program code identifying a pressure to be maintained within atube amongst the plurality of substantially evacuated tubes; (c)computer readable program code identifying, for each of a plurality ofpercentages of helium, a first power required to maintain the tubeamongst the plurality of substantially evacuated tubes at the pressureidentified in (b) and a second power corresponding to the capsule toovercome aerodynamic drag; (d) computer readable program code computing,for each of the plurality of percentages of helium in (c), a sum of thefirst power and the second power to determine a total power for thespeed identified in (a); (e) computer readable program code identifyinga helium-air ratio from an optimal value within total power valuescomputed in (d) for the speed identified in (a); and (f) computerreadable program code sending instructions to maintain within the tubeamongst the plurality of substantially evacuated tubes, a percentage ofhelium according to the helium-air ratio identified in (e).

In yet another embodiment, the present invention provides an article ofmanufacture having non-transitory computer readable storage mediumcomprising computer readable program code executable by a processor toimplement a method to determine optimum operating points for power/costand helium-air ratios in a plurality of substantially evacuated tubes ina tubular transportation system for transporting one or more passengersor one or more cargos via a capsule along a predetermined route, thenon-transitory computer readable storage medium comprising: (a) computerreadable program code identifying a speed of the capsule; (b) computerreadable program code identifying a pressure to be maintained within atube amongst the plurality of substantially evacuated tubes; (c)computer readable program code accessing a first dataset of a firstpower versus a plurality of percentages of helium, the first powerrequired to maintain the tube amongst the plurality of substantiallyevacuated tubes at the pressure identified in (b); (d) computer readableprogram code accessing a second dataset of a second power to overcomeaerodynamic drag versus the plurality of percentages of helium; (e)computer readable program code computing a third dataset of the totalpower versus the plurality of percentages of helium wherein, for each ofthe plurality of percentages of helium, a sum of the first power fromthe first dataset and the second power from the second dataset is usedto determine the total power; (f) computer readable program codeidentifying a helium-air ratio from an optimal value within total powervalues computed in (e) for the speed identified in (a); and (g) computerreadable program code sending instructions to maintain within the tubeamongst the plurality of substantially evacuated tubes, a percentage ofhelium according to the helium-air ratio identified in (f).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic of a vehicle (also referred to as pod orcapsule) within a tube-based transportation system.

FIG. 2 depicts the equilibrium mechanism where when pressure waves reachthe front of the vehicle, the right amount of air flow escapes to theback of the vehicle.

FIG. 3 depicts the choking phenomenon that results when the pressurewaves from the back of the vehicle do not reach the front of thevehicle.

FIG. 4 depicts a graph of drag versus vehicle speed which identifies thecritical vehicle speed that demarcates the pressure equilibrium scenariodepicted in FIG. 2 and the choked flow scenario depicted in FIG. 3.

FIG. 5 depicts a graph of the bypass area ratio (Bypass/Tube) versus thebypass air flow Mach number.

FIG. 6(A) depicts a scenario where an axial compressor is used at thefront of the capsule in a tube-based transportation system.

FIG. 6(B) depicts the drag as a function of the vehicle speed in thescenario of FIG. 6(A).

FIG. 7 depicts Table 2 showing the distinguishing features of lightestweight gases, of which helium and hydrogen have the lowest densities.

FIG. 8 depicts Table 3 noting a list of the speed of sound entries forvarious gases.

FIG. 9 depicts Table 4 showing the mean free path for differentmolecules.

FIG. 10 depicts a view of the 2D mesh used in the present simulations.

FIG. 11 depicts Table 5 which compares air density to helium at 100 Pa.

FIG. 12 depicts a graph showing the drag coefficient from 2D simulationfor air and helium.

FIG. 13 investigates the effect of density by plotting the actual dragfor a 3D capsule against the capsule velocity.

FIG. 14 depicts a graph illustrating power reduction based on usinglight-weighted gas.

FIG. 15 depicts the results of CFD studies comparing maximum velocitiesat the K-limit attainable due to variations in the helium-air mixtures.

FIG. 16 depicts identifying a capsule speed given a power requirementfor a specific combination of air and helium.

FIG. 17 illustrates a comparison of drag versus velocity, at theKantrowitz limit, graphs for four basic tube pressures from 1-1000 Paalong with percentages of helium in air.

FIG. 18 illustrates a power versus velocity graph where the powerrequirements are reviewed for various pressures and various air-heliummixtures to identify optimal operational ranges.

FIG. 19 illustrates a drag versus velocity graph, just as FIG. 17, butfor a lower bypass ratio of 0.208.

FIG. 20 illustrates a power versus velocity graph, just as FIG. 18, butfor the lower bypass ratio of 0.208.

FIG. 21 illustrates a comparison of two non-limiting bypass ratioexamples used in this disclosure, along with a sample calculation of howthe bypass ratio is calculated in each instance.

FIG. 22 illustrates helium in the low bypass system (0.208) does allowspeeds compared to the high bypass (0.489) region for certain gaseousmixtures of helium and air.

FIG. 23 illustrates a table depicting volume loading at 50 slm/km bypercentage of helium.

FIG. 24 illustrates a table depicting volume loading at 5 slm/km bypercentage of helium.

FIG. 25 depicts a graph of pump power (in kW) versus the percentage ofhelium for various pressures.

FIGS. 26A-C shows a summary of power requirements (kW) to balanceaerodynamic drag at a pressures of 1000 Pa, 100 Pa and 10 Pa,respectively, for various capsule speeds versus percentages of heliumand Air.

FIG. 27 depicts a graph of total power (in kW) (combining pumping powerand aerodynamic power) versus the percentage of helium for variousvelocities at 100 Pa.

FIGS. 28A-C depicts such a non-limiting example, where the same analysisas FIGS. 25-27 is performed for a leak of 5 slm/km.

FIG. 29 illustrates see how these graphs depicted in FIGS. 25-27 may becombined to provide optimum operating points for power (cost) andhelium-air ratios.

FIG. 30 shows a graph of the diffusion coefficients for various gas inair.

FIG. 31 depicts a first implementation that includes a set of heliumtanks uniformly fitted along the tube length, where helium is injectedwith controlled valves that open or close to maintain the desired levelof helium.

FIG. 32 depicts a second implementation that includes helium tanksembedded in the vehicles.

FIG. 33 depicts an approach that combines the approaches of FIGS. 31 and32.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

While this invention is illustrated and described in a preferredembodiment, the device may be produced in many different configurations,forms and materials. There is depicted in the drawings, and will hereinbe described in detail, a preferred embodiment of the invention, withthe understanding that the present disclosure is to be considered as anexemplification of the principles of the invention and the associatedfunctional specifications for its construction and is not intended tolimit the invention to the embodiment illustrated. Those skilled in theart will envision many other possible variations within the scope of thepresent invention.

As noted in the background, recent efforts to increase the capsule speedhave focused on reducing the tube pressure or improving the bypass ratiowith the use of a compressor. As mentioned previously, a reduced tubepressure does have merit at some key vacuum level, but it comes at theprice of substantial increases in vacuum pump capacity and cost. Addinga compressor to the front of the capsule has some merit, but it onlyincreases speed marginally and is also costly and complex.

The present invention overcomes the pitfalls associated with the priorart by using a mixture of air and helium (in various ratios to bedescribed later) to modify the fluid properties such as speed of sound,which enables reaching high vehicle speed at acceptable propulsionpower. Advantages of using a mixture of air and helium include obtainingdifferent fluid properties, such as, reduced density, higher speed ofsound and higher free molecular path. These different fluid propertiescan substantially reduce the drag on the vehicle and the propulsionpower needed.

It should be noted that having a lower density (by a factor of seven)has a substantial and direct effect on drag and propulsion power. Dragis directly proportional to density (and any means to reduce density isuseful in a tube-based transportation scenario), which is why aircraftfly at high altitude (low density) and which is why low-pressure tubesare considered (low density). The present invention notes another way toreach low density, i.e., by using light gases instead of standard air.In addition, the present invention goes further than just reducingdensity because it also takes advantage of higher speed of sound andhigher free molecular path as possible ways to counter the Kantrowitzlimit.

The present invention discloses mixing different gases that are lighterthan air, where these gases have smaller molecular diameter. There arenumerous gasses which meet the requirement of a gas molecule smallerthan air. The subject of this patent application is the use of helium,which has attractive properties that can be exploited in tube-basedtransportation systems. While, the air in the tube could be replacedcompletely by helium, this could be hard to achieve. Instead, thepresent invention discloses using a mixture of air and helium in variousratios (which is discussed in detail later in this patent application),which still has interesting properties, while also providing animplementation at a lower cost (when compared to previously describedprior art systems and when compared to equivalent systems that use justhelium).

It must be noted that the cost associated with replacing the aircompletely or partly by other gases may be reasonable. Since thepressure is low, about 100 Pa in standard applications, the amount ofinjected gas in the tube should remain low. Table 1 below shows the massof gas in the tube for a mixture of air and helium at differentpercentages.

TABLE 1 Length of Tube  10 km Diameter of Tube  4 m Pressure in Tube 100Pa Temperature in Tube  20° C. Mass of Gas Tube filled with air 150 kgTube filled with helium  21 kg Tube filled with (17% air;  43 kg = 25 kg(air) + 83% helium) by Volume  17 kg (helium) corresponding to (60% air;40% helium) by Mass

Table 1 demonstrates that the amount of helium to be injected in a 10 kmtube is low, whether considering pure helium or a mixture of helium andair. At 100 Pa, the entire 10 km tube could be filled with pure heliumat current cost of less than $300 (˜$14.00/kg He). However, it is notpossible to maintain a 100% helium content in a large welded tube due toleakage of air from outside the tube. It is the intent of this art todefine optimum percentages of helium and air which reduce drag in thetube.

Some of the advantages of the present invention are listed below. Gasesthat are lighter than air have a lower density, a higher speed of sound,and higher free mean path. This offers at least three advantages,simultaneously. The first advantage is the possibility of significantlyreducing the density of the gas. Since drag is proportional to thedensity, a reduction of the density of the gas directly impacts thedrag. Table 2 below shows the density at atmospheric pressure for usualgases, extracted from the website (Source: Engineering Toolbox website).

Table 2, as shown in FIG. 7, depicts the distinguishing features oflightest weight gases, of which helium and hydrogen have the lowestdensities. Helium has a density seven times lower than air atatmospheric pressure. This ratio is the same in a tube pressure of 100Pa, which means that drag can be expected to be reduced by a factor ofabout seven. This is a major advantage that goes to the root of highspeed transportation: reducing drag by reducing density.

Replacing a portion of the air by a lighter gas offers twopossibilities:

-   -   either benefit from lower density at the same environmental        pressure (therefore reducing propulsion power); or    -   operate at higher environmental pressure and achieve equal        density (therefore reducing the pumping power).

Hence, smaller diameter gases are of less density, which reduces thedrag on the capsule. The use of a combination of air and helium (inspecific, predetermined proportions, as will be detailed later) allowshigher capsule speeds, reduces vacuum pump size and cost. Such acombination of gases provides a significant improvement in high-speedtube-based transportation technology and will reduce costs, and improveeconomics, and commercial viability.

Another advantage is the possibility to increase the speed of sound. Asshown in above section, a high speed of sound allows a higher vehiclespeed without choked flow. The speed of sound for a gas is given bybelow formula:

$\begin{matrix}{c_{sound} = ( {\gamma\;\frac{R_{gas}}{W_{gas}}T} )^{0.5}} & ( {{EQN}.\mspace{14mu} 2} )\end{matrix}$where γ is the specific ratio, R_(gas) is the gas constant (8.3145J/kg/K), W_(gas) is the gas molecular mass (kg/mol) and T is thetemperature of the fluid. From EQN 2, the speed of sound can beincreased by changing the molecular mass. In particular, a lightweightgas has a high speed of sound.

Table 3, as shown in FIG. 8, is a list of the speed of sound entries forvarious gases (Source: Engineering Toolbox Website):

From Table 3, it is seen that the lightest weight gases stand out interms of their speed of sound entry. Helium and hydrogen have thehighest speed of sound. Helium has a speed of sound three times higherthan air while hydrogen has a speed of sound four times higher than air.For the purposes of this patent application, it is preferred to useHelium in the tube (since flammability issues would have to be addressedwith hydrogen, which would require some design changes).

Referring again to the example from the previously described paper toChin et al. (2015), it was shown that in a tube filled with air, maximumvehicle speed occurred around Mach 0.25, i.e. 300 km/h for air. Sincehelium has a speed of sound three times higher than air, Mach 0.25 inhelium corresponds 900 km/h. The present invention, therefore, providesa substantial gain, by only changing nature of the gas, and withoutmodifying anything else in the tube or the capsule design.

Referring to the same example, consider now a mixture of air and heliumin the tube, which might be more easily obtained. The speed of sound ofthe mixture isc=(R _(mix)γ_(mix) T)^(0.5)  (EQN. 3)where R_(mix) is the specific gas constant of the mixture, γ_(mix) isthe specific heat ratio of the mixture, and T is the Temperature. For amixture of (17% air; 83% helium) by volume, which corresponds to (60%air; 40% helium) by mass, the speed of sound is 664 m/s, which is twicethe speed of sound in pure air. Referring to the example in Chin et al.(2015), the maximum speed of Mach 0.25, which was 300 km/h in air, now,based on the teachings of the present invention, becomes 600 km/h in theabove noted mixture of air and helium. This gain is obtained without anyother change in tube or capsule design.

A simpler way to look at this makes the solution easier to understand.The Kantrowitz limit occurs when gas flowing around the capsule becomeschoked, i.e., at a speed of Mach 1. Mach 1 for air is 331 m/s atstandard temperatures. Smaller molecular gases have higher speed ofsound which allow them to flow much faster before choking. The capsulewill not be subject to choking flows until the preferred, and muchhigher Mach speed is reached.

Thus, smaller molecular diameter gas allows higher speeds before goinginto the sonic region. The geometry of the capsule and tube will stilldetermine when choking occurs, but in the case of air it occurs at therelatively low speed of 331 m/s. By switching to a gas or mixture ofgases with much higher Mach speeds, such as 972 m/s for helium, and1,290 m/s for hydrogen, much higher capsule speeds can be attainedbefore choking occurs. It is noted that the capsule does not avoid theK-limit, but the speed at which the K limit becomes a problem isincreased.

Lastly, another advantage is the possibility of increasing the free pathof the gases. If the mean free path is large enough, the assumption offluid continuum is no longer true, and the fluid must be treated bymolecular flow theory. As explained above, this opens the possibilitythat choking phenomena do not exist because the physics becomesdifferent.

The Knudsen number is used to estimate whether the gas can be treated asa continuum or as a molecular flow. Continuum is true if Kn<0.001, andmolecular flow is true for Kn>0.01. In between, a transition regionoccurs, which can also be interesting.

$\begin{matrix}{{Kn} = \frac{\lambda}{L}} & ( {{EQN}.\mspace{14mu} 4} )\end{matrix}$

The Knudsen number compares to the mean free path, λ, of the moleculesand the vehicle characteristic size L (length or diameter). Hence,molecular flow region can be attained by increasing the mean free path.

The mean free path is given by the below formula:

$\begin{matrix}{\lambda = \frac{kT}{ \sqrt{}2 \pi\;{Pd}_{m}^{2}}} & ( {{EQN}.\mspace{14mu} 5} )\end{matrix}$where k is the Botzmann constant, P is the pressure, and d is themolecular diameter.

From EQN. 5, it is seen that an increase in the mean free path isobtained by reducing the pressure, P, or reducing the moleculardiameter, d_(m).

But a key insight comes from rearranging the basic Knudsen equation(i.e., EQN. 4). A pressure term appears in the denominator of EQN. 5 andone can look directly at what pressures are required to create a Knnumber in the molecular range. Suitably low numbers of pressure docreate a large Kn number and lead us to the conclusion that pressure isagain the best path to finding the operating region in which K-limitbecomes insignificant.

The most effective Kn number can be derived not from just lowering thepressure, but rather from changing the diameter of the gas molecule,d_(m), in the denominator of the expanded free mean path (EQN. 5).

Previously, it was explained that to achieve molecular flow, thepressure had to be reduced below 1 Pa for a tube with air. This demandsvery large pump power to achieve such low pressure. Instead, by using agas with smaller diameter (light-weight gas), it is possible to increasethe mean free path. Table 4 depicted in FIG. 9 shows the mean free pathfor different molecules (Source: Pfeiffer-Vacuum website).

From Table 4 it is seen that helium has one of the highest mean freepaths, about three times higher than air. This means that it is possibleto reach the molecular flow region with a higher pressure, about threetimes higher than if it were air. Hence, in the present invention, thepump requirement to achieve molecular flow is significantly reduced.

Computational Fluid Dynamics (CFD) Simulations with a two-dimensionalconfiguration of the Tube Transportation System were performed. Theconfiguration is 2D planar. It is an approximation of the reality whichis 3D. Still, it gives a useful insight on the dependence of the drag onvehicle velocity and on gas. The 2D planar CFD provides drag coefficientat different vehicle speed. These drag coefficients can then be used toestimate the actual drag on the 3D actual capsule. Both drag coefficientand estimated drag on 3D actual capsule are presented.

The schematic of Chin et al. (2015) shown in FIG. 1 was used and a viewof the 2D mesh used in the present simulations is depicted in FIG. 10.The tube is 4 m diameter and the Bypass-to-Tube-Area Ratio is about0.489. These numbers are similar to the previous study from Chin et al.(2015). However, in stark contrast to Chin et al. (2015), the presentinvention operates at a pressure of 100 Pa, with a mixture of air andhelium. Note that the operating density of helium is about seven timeslower than air. Hence, a reduction of drag is expected by a factor of 7.

FIG. 11 depicts Table 5 which lists the density by mass figures for bothair and helium at 100 Pa. As mentioned previously, the reduction indensity of over seven times (0.00116/0.00016) reduces drag in a similarratio (i.e., seven times). This advantage holds true at differingpressures in the continuum range. (Note: Due to round off errors thebypass ratio is sometimes shown as 0.488 or 0.489)

In the results below, both the drag coefficient and the estimated dragon the actual 3D configuration are presented.

Drag, as previously noted in EQN. 1, is related to the drag coefficientbyD=C _(D)½ρ_(tube) V _(pod) ² S _(pod)  (EQN. 1)

The 2D simulations provide the Drag Coefficient at different podvelocities. The estimated 3D drag is then obtained by multiplying thedrag coefficient ½ ρ_(tube)V_(pod) ²S_(pod) where ρ_(tube) is the tubeoperating density, V_(pod) is the pod velocity, and S_(pod) is thefrontal surface area of the pod.

FIG. 12 depicts a graph showing the drag coefficient from 2D simulationfor air and helium. The drag coefficient increases substantially whenthe velocity goes above the Kantrowitz limit. It is noted that theKantrowitz limit for helium is reached at a speed about three timeshigher than that of air, which is in line with what was expected. It isalso noted that below the Kantrowitz limit, the drag coefficients ofhelium and for air are similar (about 3.5 at 375 km/h). This is becausethe drag coefficient formula is drag divided by density.

FIG. 13 investigates the effect of density by plotting the actual dragfor a 3D capsule against the capsule velocity. The graph belowillustrates the behavior of the estimated Drag of the actual 3D pod forhelium and air. The 3D drag is estimated using 2D Drag Coefficients andmultiplying it by ½ ρ_(tube)V_(pod) ²S_(pod).

The graph in FIG. 13 confirms two important claims of the presentinvention:

1. Benefits of Low Density

Consider the region of Vehicle Velocity below the Kantrowitz limit ofboth helium and air. The drag of helium is lower than that of air. Forthe same pod speed of 300 km/h, the drag with helium is about 5.5 timeslower than with air. This is close to the ratio of density of 7 betweenair and helium.

2. Higher Speed Before Reaching Kantrowitz Limit

The Kantrowitz limit Velocity for helium is about three times higherthan that of air. Above the Kantrowitz limit, the drag starts risingsubstantially with velocity due to choking. Results shown in FIG. 13confirm that helium can go to a velocity three times higher than that ofair before reaching the Kantrowitz limit. Hence, helium can go to avelocity three times higher for a reasonable demand of power. Helium,therefore, can allow a capsule speed of nearly 1,000 km/h before thenecessity of overcoming the Kantrowitz limit.

The benefits of low drag directly correspond to lower power requirementsfor propulsion. Lower power equates to less operating cost which is akey to putting this technology into practice. Less cost provides cheapertickets and more ridership bringing this technology to mainstreamadoption.

FIG. 14 depicts a graph illustrating power reduction based on usinglight-weighted gas, where the graph compares requirements to overcomeaerodynamic drag with air versus helium (at 100 Pa). The same power tooffset aerodynamic drag can achieve speeds of over 900 kph in ahelium-based system but can only achieve 425 kph in an air-based tube.Twice the speed is achieved for the same cost in aerodynamic power.

Therefore, replacing air or part of air in the tube by light-weightgases provides at least the following advantages: lower density (and,hence, lower drag, implying lower propulsion power), higher speed ofsound (and, hence, higher vehicle speed before occurrence of the chokingphenomenon), and higher mean free path (and, hence, lower pump power toachieve molecular flow as molecular flow may avoid choke phenomenon andthus decrease propulsion power).

As explained previously, implementing a mixture of air and light-weightgases, such as helium, in the tube can substantially reduce the drag onthe vehicle and in turn the propulsion power needed to overcome drag.Some further charts are valuable in determining the optimum mixturepercentages and pressure ranges of air and the light-weight gas.

FIG. 15 depicts the results of CFD studies comparing maximum velocitiesat the K-limit attainable due to variations in the helium-air mixtures.Drag is a useful indicator to chart against velocity as there is noeconomic advantage to achieving higher speeds if the drag increasescorrespondingly.

At 100 Pa tube pressure, we see the increasing speeds attainable withincreasing helium percentages. The dashed vertical lines show the speedat the K limits, first, on the left, for pure air and lastly for purehelium. The second vertical line, on the right, is for a 100% by volumehelium filled tube and shows a maximum speed of exceeding 1,200 km/hrwith an only nominal increase in drag. Comparing that to the air maximumspeed line it is noted that the achievable speed has increased nearlythree times from 425 km/hr to over 1,225 km/hr.

As mentioned previously, the operational cost is a function of power.Choosing an optimal speed with reference to cost can be qualitativelyseen from the power versus gas mixture graph shown in FIG. 16. Forexample, given a power potential of approximately 27 kW, a targetvelocity of 800 km/hr may be achieved using a gaseous mixture of 5%air+95% helium.

Speed is nearly doubled (when compared to pure air) with the same powerusing a conservative 95% helium/5% air mixture. Additionally, thismixture allows much higher capsule speeds, but at the cost of higherthrust power. This is an important consideration as it is anticipatedthat in long and remote sections of the route it will be necessary topower the propulsion from the capsule. This can only be provided byonboard power until improved methods of non-contact power transferbecomes proven. Thus, keeping power low allows the use of smaller andlighter capsule power packs. Maximum speeds do not guarantee optimumoperation costs as the economics rely on the length, curvature andelevation changes within the route and the source of propulsion power.

Performance with light-weighted gas has been shown primarily at 100 Papressures to keep the discussions similar and, also, due to the ease ofmaintaining this vacuum. But, there is a much wider range of pressuresachievable that have trade-offs. Results for different ranges ofpressures are next presented as we further optimize gas percentages withoperating pressures.

FIG. 17 illustrates a comparison of drag versus velocity, at theKantrowitz limit, graphs for four basic tube pressures from 1-1000 Paalong with percentages of helium in air. First, it is noted that thevelocity at Kantrowitz Limit increases as the percentage of heliumincreases in the mixture, for all pressures. The increase in velocity atthe Kantrowitz limit has a relatively low dependence on pressure. Now,different graphs for various pressures are examined. These pressurecomparisons are first made on the basis of drag and are most interestingfor the lowest pressure regime, 1 Pa, where the low pressure and highhelium percentage transforms the flow to laminar, thus increasing drag80% in the 1-100% helium range. The 1000 Pa tube is also seen to createvery high drag despite all combinations of air and helium. This willcertainly result in high propulsive power requirements leading toimpractical capsule onboard energy storage systems.

It is seen from the 1 Pa pressure graph that drag, in spite of laminarflow, is quite low and power requirements will also be low. But, thepumping power to achieve that vacuum level, combined with expected airleakage rates (45 SLM (standard liter per minute)/km), will result inthat pressure not being viable without major, and more than offsetting,costs in capital expenditures.

At higher pressures, such as 10 Pa, we see that the drag increasesminimally as the vehicle speed more than doubles. This is a criticalpoint to consider. Drag is one of the key consumers of power that mustbe overcome by the propulsion system, the others being acceleration andgravity. Once the vehicle is at operational speed and running on levelterrain, drag is the major drain on power consumption for propulsionpurposes. Thus, economic operation depends on minimizing drag at thehighest operation speeds and obtainable vacuum levels. Notice above thataerodynamic drag is shown to be increasing at a low rate (<25%) withsignificant speed increases. Operation at higher speeds is achievablewith only incremental drag increases. Current high-speed rail does nothave this advantage and thus is constrained to lower speeds or muchhigher power requirements or both.

FIG. 18 illustrates a power versus velocity graph where the powerrequirements are reviewed for various pressures and various air-heliummixtures to identify optimal operational ranges. Aerodynamic powerconsumption graphs with varying helium percentages at pressures of 1,10, 100 and 1000 Pascals are shown.

Based on extensive CFD runs, proven gas properties and behavior atvarious pressures, we can narrow our operating ranges based on powerrequirements. This is the primary factor in determining operatingcosts—how much energy is required and practical—to operate at highspeeds. The power ranges depicted in FIG. 18 for 100 Pa and 10 Pa areachievable with current battery technology for onboard storage systems.Existing Li-Ion batteries used in cars have capacity of 30-100 kwh andthus with several of these packs would be suitable to sustain capsulepropulsion (to overcome shown aerodynamic drag) for smooth and straightroutes and have suitable safety reserves. As mentioned previously,variations in elevation and curve radii will all affect the powerrequirements, as will drag due to other elements of propulsion,life-support, etc. Due to limited volume and available weight forbattery storage capacity on board the capsule, the opportunity to reducebattery power is closely examined and must be compared to the increasedvacuum pumping power to obtain those lower pressures. At this very largescale, low power regimes can be achieved with modest percentages ofhelium and at reasonable vacuum levels.

The present invention identifies that helium percentages in air rangingfrom 75%-99% are practical and effective for increasing capsule speedsfrom a base of 400 kph in pure air to as high as 1,150 kph in a mix of99% He and 1% air. Lower percentages of helium also provide improvementsas shown, but due to the relative low cost of helium, do not provideoptimum or most cost effective operating points. Helium percentages inthe 75%-99% range are practical to control with current state-of-the-artmass flow controllers, sensors and control systems.

The present invention also shows optimum tube pressures which areeconomical to achieve, ranging from 10-100 Pa. Pressures below 10 Pa,such as 1-10 Pa, show promise in reducing drag, but move into the rangeof laminar flow and transition to a lower maximum speed at K limit. Itis apparent, however, that even at these very low-pressure ranges below1-10 Pa, helium shows an increase in attainable speeds and thus thisoperational environment will gain improvement from the addition ofhelium from the speed perspective. But, it is similarly interesting thatthe change in power requirements is very little compared to a pure airsystem. Thus, the range of power at 1 Pa with and without helium is only0.5 to 2.5 kW. A light-weighted gas system does not derive muchincremental advantage at these pressure ranges (1-10 Pa) in thedrag/power regimes. However, top speeds do enjoy a large incrementalincrease of 400 kph to 1,150 kph and thus it is expected that operationsbelow 10 Pa will also include large percentages of helium similar to theranges at 10 to 100 Pa.

All of the previous analysis was performed with a bypass ratio of 0.489(4 m tube diameter and 6.4 m² pod area) and showing examples ofpressures and helium percentages for optimum performance. Now, adifferent bypass ratio is analyzed.

FIG. 19 illustrates a drag versus velocity graph, just as FIG. 17, butfor a lower bypass ratio of 0.208. FIG. 19 depicts a low bypass systemof 0.208 (4 m tube diameter and 10 m² pod area) and its aerodynamic dragimprovements due to use of light-weighted gas mixtures. The advantagesof larger bypass ratio can be clearly seen in any of the above pressuregraphs as the attainable speeds are more than double with the 0.489bypass vs 0.208. Top speed will be a major advantage on long routes andthus larger bypass ratios preferred, but on short routes the speedadvantage is diminished, and smaller ratios may be acceptable. Likewise,smaller bypass ratios may be relevant for low-speed cargo operationsduring off hours and enables the use of larger cargo capsules in thesame tube. Although top speeds are reduced with the smaller bypassratio, the advantages over pure air systems are still attained.

It is worth noting that for these two quite different bypass ratios of0.489 and 0.208, the power requirements stay within similar ranges. Thedifferent bypass ratios impact the maximum speed more than the power. Ascapsule power may be limited (e.g., due to battery energy density andspace available), the low bypass system will be capable of operatingunder such limited power, but at the disadvantage of much reducedspeeds.

FIG. 20 illustrates a power versus velocity graph, just as FIG. 18, butfor the lower bypass ratio of 0.208. Just as in FIG. 18, the powerrequirements may be reviewed for various pressures and variousAir-helium mixtures to identify optimal operational ranges. Due thehigher drag of the low ratio systems at same speeds, more power isrequired to attain the same speed. However, with the 0.208 bypasssystem, maximum speeds are still significantly increased over 100% airsystems.

FIG. 21 illustrates a comparison of two non-limiting bypass ratioexamples used in this disclosure, along with a sample calculation of howthe bypass ratio is calculated in each instance. It should be noted thatwhile this disclosure uses two bypass ratios, i.e., 0.489 bypass ratiofor a capsule to transport humans and 0.208 bypass ratio for a cargocapsule, these ratios should in no way be used to limit the scope of thepresent invention, as the teaching of the present invention can beapplied to other bypass ratios.

As seen in FIG. 22, using helium in the low bypass system (0.208) doesallow speeds compared to the high bypass (0.489) region for certainmixes, as indicated by the velocities bounded by the dotted lines inboth the 10 Pa and 100 Pa graphs.

Much can be deduced about optimum operating conditions from comparingthe power for the two different bypass ratios as seen in FIG. 22. Firstof all, the maximum speed attainable (before K-limit) with low bypass isseverely reduced. Even at the lowest of tube pressures (1 and 10 Pa) itis seen that even with 100% helium, the attainable velocity is only halfof the velocity with much lower He percentages that incorporate thehigher bypass ratio. Second, for the smaller bypass ratio, those lowervelocities are all at nearly three times the power than similar speedsutilizing a higher bypass ratio. It is, therefore, noted thatoptimizations of capsule-to-tube geometry, creating the largest bypasspossible, result in much greater speed with much less power.

Greater system operational flexibility for speed and power is achievedby adding specific mixtures of Air and helium for either of thedescribed bypass ratios. For lower bypass ratios (i.e., 0.208)equivalent speeds to high bypass ratios (i.e., 0.489) can be obtained asseen in the figures above between the vertical dashed arrows.

At tube pressures of 10 Pa and 100 Pa, ranges of equal speed for bothbypass ratios are shown. At 100 Pa, the drag in the small bypass ratioscenario increases almost three times at the same speed, but only byadding 75-100% helium. For larger bypass, equal speeds are attainable,but with a third of the drag. Adding helium helps significantly for thesmall bypass system scenario (versus a pure air system), where such anaddition can be leveraged for larger capsules, such as cargo types. Suchaddition of helium allows nearly three times the speed (when to comparedto a pure air system), with only marginal increases in drag. Asignificant speed penalty is paid for by the smaller bypass system asthe maximum speed is limited to about half of that of the larger bypasssystem. Using much lower pressures (e.g., down to even 1 Pa) does notovercome the overwhelming advantages of large bypass systems.

A key to putting He-Air mixtures for high-speed tube travel intopractical use is narrowing the proper mixture percentages based on aneconomic model. That process is outlined next and identifies clearly whymany higher percentages of He are not optimal, and which ranges are noteven achievable.

While higher percentages (e.g., 99% or 100%) of helium are preferred, itshould be noted that such higher percentages are not possible withcommercial pipe construction, due to residual air leakage through welds,joints, feedthroughs, and material imperfections. The amount of airleakage does not change with tube pressure as each leak can be modeledlike an orifice. In this model, each orifice follows standard gas lawsand chokes at pressures drops above approximately 0.53 ΔP and will belimited to flow at sonic speeds. The choking of each orifice maintainsconstant flow up to a tube pressure approximately 53,700 Pa. Tubepressures in the region of 1-1000 Pa essentially creates equal airleaks. Thus, each of these orifices will contribute small amount of Airinto the vacuum vessel which must continuously be pumped if basepressure is to be maintained. This continuous leakage makes achieving100% He content impossible unless a perfectly leak tight tube can bedesigned. However, practical implementations of such tube-basedtransportation systems will suffer from the effects of these leaks,making reaching 100% helium not a practical solution.

A range of leaks that can be expected per km of tube is noted based onexperience of experts in the field and under conditions seen with otherlarge tube vacuum systems. For this patent disclosures, the upper rangeof 50 slm/km (standard liter per minute/km) is chosen as a worst case,and 5 slm/km a best case. FIG. 23 illustrates a table depicting volumeloading at 50 slm/km by percentage of helium. FIG. 24 illustrates atable depicting volume loading at 5 slm/km by percentage of helium. Suchleak rates are merely provided as examples and should not be used tolimit the scope of the invention. A discussion is now presentedregarding how this leak rate must be accounted for in calculatingpreferred helium ratios as well as ideal operating pressure.

This leak rate is directly related to methods and materials ofconstruction of the tube, where with knowledge of such methods andmaterials, one can populate Table in FIG. 23 or 24 with more accuratenumbers. The leak rate may be calculated using standard vacuum systempractices and should be measured for each part of the route. Suchestimated data associated with different portions of the route iscritical in estimating base tube pressures and percentages of heliumthat can be reasonably achieved within each portion of the route.

As seen above in FIGS. 23 and 24, with increasing helium percentages,the Added Volume column increases geometrically at constant leak rates.Very high percentages of helium require increasing amounts of injectedhelium where such injected amounts approach infinity as the heliumrequirement reaches 100%. This added volume of air/helium mixture mustbe pumped out to maintain required vacuum levels, and thus may load thepumps beyond their capacity. Although from earlier discussions itappears that higher percentages of helium are always preferred there isa counter trend of increasing pump loads that must also be considered.

FIG. 25 depicts a graph of pump power (in kW) versus the percentage ofhelium for various pressures. As can be seen from FIG. 25, vacuum pumpsare very sensitive to volumetric flow rates with power (kW), increasingin a geometric fashion at He-Air percentages beyond approximately 90%.These pumping power curves show the diminishing returns of trying tomaintain high percentages of helium with respect to pumping power (kW).This deleterious effect is most pronounced at low tube pressures whichis counter to the desire to operate at low pressure to reduce drag. FIG.25 shows the negative effects of high helium percentages versusnecessary pump power to maintain those percentages. More is not better.The present invention leverages this effect to achieve optimumperformance within a tube-based transportation system. In oneembodiment, the most economical operating percentages can be deducedwhen coupling this result with the power required to overcomeaerodynamic drag.

There is a complex interaction of tube pressure, speed, bypass ratio,Air leakage, He-Air %, drag and pump power which heretofore has not beenpresented in an organized manner in the prior art. All these physicalparameters constrain the ideal operating speed. Those key tradeoffs havebeen analyzed in several typical regimes and now can present a systemand method of finding optimum operating conditions. The number ofcombinations is vast, but by simulation and using physical properties,while operating in typical or expected ranges of those regimes, one canformulate the most practical and economic use of a tube-basedtransportation system.

The present invention discloses a system and method for identifyingoptimum He-Air ranges based on the economics of power usage, both forpumping the tube to vacuum, and also for overcoming drag at operationalspeeds. Ideally, 100% He results in the lowest drag and highest speedsdue to its reduced molecular size (improved speed) and lower density(reduced drag). The calculations following show that not only is 100%helium not possible.

First, particular pump curves are required to be derived for a 1 kmlong, 4-meter diameter steel pipe at various base pressures. Thesecurves include an allowance for air leakage of a 50 slm of Air per km.As noted earlier, such a leakage rate is merely provided as an exampleand should not be used to limit the scope of the present invention.Since the basis for optimization is power consumption, the curves showthe amount of pumping power required to keep the tube at constantpressure (as depicted in FIG. 25), based on a given leak rate. Differentleak rates will change the graph, but the conclusion will always showthat at higher He ratios the pumps must operate at higher and higherpower to evacuate the increasing volume of the He-Air injected. As thepercentage of helium required within the tube increases, incrementallylarger amounts of He must be injected to maintain the ratio. The higherthe percentage of helium, the more power the pumps require.

Next, the power required to overcome drag at various speed andpercentages is examined. FIGS. 26A-C shows a summary of powerrequirements (kW) to balance aerodynamic drag at a pressures of 1000 Pa,100 Pa and 10 Pa, respectively, for various capsule speeds versuspercentages of helium and Air. As noted previously, the highest speedscan only be attained with the highest percentages of helium. It is seenhere that capsule/propulsion power (aerodynamic drag×velocity) isreduced significantly at the highest percentages of helium. But as shownin FIG. 25, those helium rich environments come at the cost of muchadded pump power. These two interactions need to be combined toformulate the least power and best operating points. FIG. 27 depictssuch a combination by way of a graph of total power (in kW) (combiningpumping power at a given leak rate and aerodynamic power) versus thepercentage of helium for various velocities at 100 Pa.

Before continuing it may be helpful to discuss the impact of varying airleak rates on the present invention's optimization system and method.Leaks affect the pump capacity in two key areas. An order of magnitudesmaller leak can allow an order of magnitude lower pressure attainablein the system. Thus, lowering the leak rate is a very efficient methodof achieving lower tube pressures. The same relation is seen betweenpump power and leak rate as the power can be reduced (theoretically) anorder of magnitude at the same pressure if the leak rate is reduced by afactor of 10. The present invention's disclosure uses a non-limitingexample of 50 slm/km air leakage, but the specific air leakage numbershould not be used to limit the scope of the present invention. However,it should be noted that the teachings of the present invention may beapplied to another leak rate, e.g. 5 slm/km, without departing from thescope of the invention.

FIGS. 28A-C depicts such a non-limiting example, where the same analysisas FIGS. 25-27 is performed for a leak of 5 slm/km. FIG. 28A depicts agraph of pump power (in kW) versus the percentage of helium for variouspressures for an air leak of 5 slm/km. FIG. 28B depicts a graph of thecapsule power (in kW) at 100 Pa. Since capsule power is not dependent onleak rate this is the same as graph 26B previously shown. FIG. 28Cdepicts a graph of total power (in kW) (combining pumping power andaerodynamic power) versus the percentage of helium for variousvelocities at 100 Pa for an air leak of 5 slm/km. These calculations forthe 5 slm/km leak rate validate the effect on the optimization model.

It should be noted that graphs depicted in FIGS. 25-27 relate to abypass ratio of 0.489 but, similar, but smaller effects, may be obtainedfor bypass ratios lower than 0.489. The basis of the method is toseparate the various inputs, look at the effect of He-Air mixtures onthose inputs, then to combine the inputs into a simple graph showingideal operating conditions. The graphs shown in FIG. 27 summarizeresults presented in FIGS. 25-26 by combining them to allow finding theoptimum helium-Air percentages. These are done for expected velocitieswith pressure of 100 Pa and 0.489 bypass ratio, including as assumptionof a 50 slm/km leak.

The graphs in FIG. 27 depicts fairly flat power requirements at 600, 700and 800 km/h up to 90% He mixtures. Looking closely at the graph in FIG.27 (and using the data behind the graph to identify more precisely), itis seen that 75%-85% helium in the tube appears acceptable. An operatorwould not want to operate at 75% He and 800 km/h, however, as therewould be very little safety margin before reaching the K-limit andensuing shock in the bypass area.

FIG. 29 illustrates see how these graphs depicted in FIGS. 25-27 may becombined to provide optimum operating points for power (cost) andhelium-Air ratios. FIG. 29 shows an optimum helium operating point at600 kph based solely on power requirements—least cost per km for tubepressures of 100 Pa for this set of speeds. This could be considered themost economic (or eco mode) at that pressure and set of speeds. The sameoptimization can be done at 700 kph requiring 80% of helium and 20percentage of Air, with nearly 50% more power expended, but resulting inshorter transit times by 17% (based on increasing the speed from 600km/h to 700 km/h). We see nearly a maximum operating speed of 1,000 kphrequiring over three times the power when compared to 600 kph (145 kW vs40 Kw), and requiring a 90% helium and 10% air mixture, but which willresult in reducing transit times by 67% (based on increasing the speedfrom 600 km/h to 1,000 km/h).

The restrictions of operating at 1,000-1,100 km/h can be identified bywitnessing the need for vastly increased power while also being verysensitive to small changes in the helium-air mixture. While these veryhigh speeds are achievable for this condition, bypass ratio, andpressure, such high speeds may not be not ideal. A practitioner wouldprefer to reduce the tube pressure or increase the bypass ratio if theywanted to safely and reliability operate in that region. It should benoted that while FIG. 29 is provided merely as an example for specificpressures, velocities, and bypass ratios, similar graphs can be createdfor other pressures, velocities, specific geometries, to derive theoptimum conditions for other operating points in a similar manner.

It is seen that helium concentrations in the high range are desirablebut come at a higher cost with respect to power. Also, in oneembodiment, the present invention envisions maintaining, or creating,ideal helium-air ratios from both a safety and profit point of views. Inthe described examples, power consumption has been used as an analog forprofit, however, there are several operating power points which may bechosen depending on the motives of the operator. For example, minimumpower does not occur at maximum speeds, and thus lengthens the triptime. Some operators (military, medical transport, etc.) may choose the‘optimum’ power to attain maximum speeds. The methods as per the presentinvention identify what percentages of helium are required to achievesuch maximum speeds. On the other extreme is operation at minimum powerwhich provides the longest capsule battery life and allows longer routeswhere trackside power is not available. There will often be a mid-powerrange, an ‘affordable’ power that allows some higher speed operationsbut still allows increase in the route length. Route calculations relyon the length, curvature and elevation changes within the route and thesource of propulsion power. Differing motives of operation will dictatewhat percentage of helium is ideal based on the route and whetheroperating at ‘optimum’, ‘minimum’ or ‘affordable’ conditions.

In order to optimize for this embodiment, one needs to focus not only onhelium percentages, but also on the helium distribution in the tube, andmethods to control such distribution. Similar optimizations can be donefor 1-1000 Pa and large to small bypass ratios using examples as shownearlier. Power requirements for all combinations of pressure, bypassratio, leakage, air-helium percentages and velocities can be computedbased on the teachings of the present invention. In one embodiment, thisprocess is fully automated with software, whereby optimum speeds andhelium-air ratios are quickly determined. As compared with the effortto: change the capsule or tube size (which affects bypass ratio),increase the number and size of vacuum pumps (to reduce pressure), add acompressor to the front of the capsule (to improve bypass ratio), orchange tube construction methods (to reduce air leakage), the process ofadding helium to the tube is certainly a very cost effective and simplemethod of improving tube-based transportation system performance. Usinghelium to optimize improves both capital and operational economics.Using these new techniques, identifying and operating in these optimumspots, and even varying the percentage of helium based on changingoperations (passenger vs cargo), can be automated and implemented duringdaily operations.

It is seen that the percentage of helium is a major determinant ofmaximum speed and least power along with bypass ratio, air leakage, andtube pressure. Thus, the distribution and percentages of thelight-weight gas within the length of the tube is an importantconsideration to maintain these advantages. The ability to maintain thatpercentage of helium and homogeneity within the tube is important toachieving these advantages. However, we also see that much higherpercentages of the light-weight gas are sometimes desired or required.Different portions of a route may be speed constrained due to curves,stations, elevations changes, etc., while other portions of the routewill allow maximum speeds. A homogeneous mixture must be attainable, butthere several conditions under which the most helium rich mixtureeconomically attainable is preferred, such as high-speed sections of theroute. Methods of achieving both homogeneous and enriched He atmospheresare described below.

A description of the technologies that enable to maintain a homogeneous,or light-weight enriched, mixture of gases in the tube is provided.

First, consider some standard components of the transportation system:

-   -   1. The vehicle which carries passengers or cargo    -   2. The tube that guides and encloses the vehicles    -   3. The pump that maintains low pressure in the tube and        compensates for Air leaks (from atmosphere to the tube)

The present invention proposes additional components to create and tomaintain a homogeneous mixture of gases and additionally how to improvesome tube areas resulting in increased local percentages of light-weightgases.

A list of components necessary to achieve the system is given below:

-   -   1. A source of gas (other than air)        -   a. One or many gas tanks integrated on the tube side,            distributed along the tube length whose position may be            determined by the capsule speed in that tube location,        -   b. A series of pipes connected from the gas sources to the            tube sides, with injection points distributed along the tube            length whose position may be determined by the capsule speed            in that tube location,        -   c. One or many gas tanks in each vehicle or in some            vehicles, located at known critical geometry locations on            the capsule which are most prone to shock or disturbances            from high speed flow surrounding the capsule. These            specifically are near the nose such that light-weighted gas            concentration can be increased as the flow begins its            movement over the capsule body, along the capsule body at            points where flows are near the critical K-limit, near the            tail to reduce shock waves and instability created therein,            and finally at the tail to increase the gas concentration in            preparation for any following capsule.    -   2. A system to inject light-weighted gases that is comprised of        a valve, regulator, mass flow controller, electronic controls        and injector nozzles located in any of several locations within        the hyperloop system. This system is under control of the        operations control center which is continuously monitoring gas        concentrations within the tube and supplying commands to the        injection system on proper amounts to inject in order to        maintain optimum gas ratios.    -   3. A system to recycle gas. A system integrated into the pumping        system, which separates light-weighted gases from the air/gas        mix, so that they are not exhausted to atmosphere but are        recycled back into the tube. This is comprised of an air        separation unit or membrane style gas separation unit which        takes the vacuum pump exhaust from the tube and separates out        the light-weighted gases for recycling into the gas injection        system or to a storage system for future use when the preferred        gas ratio is out of balance.    -   4. A system to monitor gas pressure and gas concentrations        including gas sensors, a data feedback and logging function plus        a data control system.        -   a. A network of pressure transducers and gas concentration            transducers integrated along the tube and/or in the            vehicles.        -   b. The output from these transducers is sent to the OCC unit            which uses software algorithms to compare measured vs ideal            concentrations and responds with control outputs to the gas            injection system.        -   c. The gas control system further has optimization routines            to provide closed loop control of required gas            concentrations and homogeneity based on sensor output.        -   d. Off the shelf gas type sensors may be used, where they            could be located on the capsule, at points along the tube,            or on the vacuum piping at the pump stations. Their output            would be directed toward an Operations Control Center (OCC)            to track deviations from ideal, changes to perform by gas            injection equipment, and results of those changes.

It should be noted that the actual implementation can be as modular aspossible, to combine a plurality of the aforementioned components.

The methods used to place the preferred gases into the tube is an areato optimize. Multiple methods are envisioned for filling the tube withthese gases. Individual and/or combined methods such as injectionthrough the tube wall, injection from the capsule, from valves placedonto the tube or tube attachments, from the capsule, or potentially fromthe vacuum pumping system all are viable methods.

Injecting the small diameter gas through various critical points in thecapsule has some potential significant advantages to enrichen the heliumcontent in localized areas around the capsule to reduce shock waves,turbulence, and possible capsule instability due to these factors. Itcan also be surmised that capsules in the tube behind a lead injectingcapsule may benefit significantly by these same factors. Such a methodof optimized capsule shell injection is another advantage of the presentinvention.

One important challenge is to compensate for Air leaks, coming from theatmosphere. Air leaks tend both to increase the tube pressure and tochange the concentration of gases (increasing the concentration of air).At these vacuum levels, there are conventional air leak rates that havebeen identified for welded steel piping. As mentioned previously, theestimate from one expert in this science, Leybold Vacuum, is a rate of45 standard liters per minute based on a 4 m diameter tube of 1 kmlength. Thus, achieving a 100% helium filled tube is not practical usingaccepted fabrication and materials. Comparing that leak rate of 45slm/km (0.05512 kg/km) to the volume of helium in the tube provides aqualitative answer to the level of helium purity attainable.

Fortunately, there is no leak of gases escaping from the tube to theatmosphere because the tube pressure is so low compared to atmosphericair. The only way the gases can leave the tube is due to the pumpingsystem that pumps the tube fluid to decrease its pressure. At the sametime, it removes the gas from the tube.

One must carefully design the whole system so that the gases can berecycled and re-injected in the tube, as needed. For example, a gasseparator can be coupled to the pumping system. It would separate airand re-inject the recuperated gas. Concerning the previous example ofhelium, there exist Air/helium separators on the market, although todaytheir practical applications are limited.

Novel methods of capturing the vacuum pump exhaust and separating outthe smaller diameter gases through typical air separation units or othertypes of separation could be used to recycle the gas back into the tubeand are also envisioned as part of the present invention.

Additionally, there are certain methods to introduce the gas into thetube that are preferred, such as to evacuate the tube and refill itpartially with the preferred gas. Several repetitions of this pump andbackfill can be done until the percentage of preferred gas or gasmixture is at the proper level. Such methods are also envisioned as partof the present invention.

Mixture homogeneity is another challenge. Homogeneity can be ensured bythe uniformly spaced reservoirs of gas, or gas tanks. Homogeneity canalso be ensured by the motion of the vehicle, possibly creating vorticesand/or turbulence in their wake that mix the gases.

Lastly, the diffusion coefficient is a good indicator of the ability ofa gas to mix into air. The diffusion coefficient of a gas in air is thecapacity of a gas to homogenize in still air, without stirring orturbulence. FIG. 30 depicts a graph of the diffusion coefficients forvarious gas in air (source: Engineering Toolbox website). FIG. 30 showsthat light-weight gases, such as helium and hydrogen, have much higherdiffusion coefficients in air than other gases. At ambient temperature,helium has a diffusion coefficient almost four times higher than methaneor water vapor with hydrogen being slightly superior. This makes heliumand hydrogen the best candidates to obtain and maintain a homogeneousmixture within the tubes.

Described below are two possible implementations of a tube withhelium/air mixture. FIG. 31 depicts a first implementation that includesa set of helium tanks uniformly fitted along the tube length, wherehelium is injected with controlled valves that open or close to maintainthe desired level of helium. The pumping system is linked to a separatorsystem that removes air and re-injects helium in the tank. For a systemwithout losses, the helium that left the tube because of the pump isconstantly refilled in the tank.

FIG. 32 depicts a second implementation that includes helium tanksembedded in the vehicles. The tanks open helium release via commandcontrol. The helium can be released in the wake of the vehicle, takingadvantage of the vortices for good mixing. The helium tank can be filledwhen vehicles are docked. Helium is collected by the separation systemintegrated in the Pumping System.

Since the present invention's approach is modular, it is possible tocombine the first and the second implementations to get a third one withhelium Tanks, both along the tube and in the vehicles. FIG. 33 depictsan approach that combines the approaches of FIGS. 31 and 32.

The embodiment depicted in FIG. 31 involves injection of the gases ormixtures directly into the tube via ports connected to mass flowcontrollers and valves, supplied by gas lines or compressed gas bottles,to precisely control the amounts of each gas introduced. The amount willbe dependent on analysis of the gases within the tube and controlled bythe Operations Control Center (OCC). The spacing of these injectionpoints needs to be engineered. It may be that injecting He into the tubejust in front of the moving capsule will aid the capsule aerodynamics.Injecting He, such that its percentage is very high as the capsuleapproaches the injection point could aid in reducing shock waves and inreducing drag.

The embodiment depicted in FIG. 32, i.e., capsule body injection, uses,in one embodiment, compressed gas bottles inside the capsule to injectthe gas or gas mixture in front, along the body, at the rear or acombination of points along the capsule. This design would moreprecisely inject the gases to areas most susceptible to drag and shockaround the capsule.

The embodiment depicted in FIG. 33 combines the teachings of theembodiments depicted in FIG. 30 and FIG. 31.

The system and processes of the figures are not exclusive. Othersystems, processes and menus may be derived in accordance with theprinciples of the invention to accomplish the same objectives. Althoughthis invention has been described with reference to particularembodiments, it is to be understood that the embodiments and variationsshown and described herein are for illustration purposes only.Modifications to the current design may be implemented by those skilledin the art, without departing from the scope of the invention. Asdescribed herein, the various systems and processes can be implementedusing hardware components, software components, and/or combinationsthereof.

For example, the feature of maintaining within each tube (in a pluralityof substantially evacuated tubes) particular percentages of helium andair can be implemented in software process where a processor (orcontroller) executes instructions to control mechanisms, such as valves,to release specific percentages of helium or release specificpercentages of helium and air. Also, as another example, the feature ofpicking a percentage helium based on a predetermined power value and aleak rate associated with each tube can be implemented in softwareprocess where a processor (or controller) executes instructions storedin storage to identify such a percentage of helium. As another example,the feature of picking a percentage helium based on a predeterminedpower value that is a function of both pump power and power to overcomedrag and a leak rate associated with each tube can be implemented insoftware process where a processor (or controller) executes instructionsstored in storage to identify such a percentage of helium. As yetanother example, the feature of picking a percentage helium based on apredetermined power value, a desired speed of the capsule, and a leakrate associated with each tube can be implemented in software processwhere a processor (or controller) executes instructions stored instorage to identify such a percentage of helium. One of skill in the artwill see that many other features described above may be implementedusing hardware, software, or a combination of both.

The above-described features and applications can be implemented assoftware processes that are specified as a set of instructions recordedon a computer readable storage medium (also referred to as computerreadable medium). When these instructions are executed by one or moreprocessing unit(s) (e.g., one or more processors, cores of processors,or other processing units), they cause the processing unit(s) to performthe actions indicated in the instructions. Embodiments within the scopeof the present disclosure may also include tangible and/ornon-transitory computer-readable storage media for carrying or havingcomputer-executable instructions or data structures stored thereon. Suchnon-transitory computer-readable storage media can be any availablemedia that can be accessed by a general purpose or special purposecomputer, including the functional design of any special purposeprocessor. By way of example, and not limitation, such non-transitorycomputer-readable media can include flash memory, RAM, ROM, EEPROM,CD-ROM or other optical disk storage, magnetic disk storage or othermagnetic storage devices, or any other medium which can be used to carryor store desired program code means in the form of computer-executableinstructions, data structures, or processor chip design. The computerreadable media does not include carrier waves and electronic signalspassing wirelessly or over wired connections.

Computer-executable instructions include, for example, instructions anddata which cause a general purpose computer, special purpose computer,or special purpose processing device to perform a certain function orgroup of functions. Computer-executable instructions also includeprogram modules that are executed by computers in stand-alone or networkenvironments. Generally, program modules include routines, programs,components, data structures, objects, and the functions inherent in thedesign of special-purpose processors, etc. that perform particular tasksor implement particular abstract data types. Computer-executableinstructions, associated data structures, and program modules representexamples of the program code means for executing steps of the methodsdisclosed herein. The particular sequence of such executableinstructions or associated data structures represents examples ofcorresponding acts for implementing the functions described in suchsteps.

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. The essential elements of a computer area processor for performing or executing instructions and one or morememory devices for storing instructions and data. Generally, a computerwill also include, or be operatively coupled to receive data from ortransfer data to, or both, one or more mass storage devices for storingdata, e.g., magnetic, magneto-optical disks, or optical disks. However,a computer need not have such devices. Moreover, a computer can beembedded in another device, e.g., a controller, a programmable logiccontroller, just to name a few.

In this specification, the term “software” is meant to include firmwareresiding in read-only memory or applications stored in magnetic storageor flash storage, for example, a solid-state drive, which can be readinto memory for processing by a processor. Also, in someimplementations, multiple software technologies can be implemented assub-parts of a larger program while remaining distinct softwaretechnologies. In some implementations, multiple software technologiescan also be implemented as separate programs. Finally, any combinationof separate programs that together implement a software technologydescribed here is within the scope of the subject technology. In someimplementations, the software programs, when installed to operate on oneor more electronic systems, define one or more specific machineimplementations that execute and perform the operations of the softwareprograms.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,sub programs, or portions of code). A computer program can be deployedto be executed on one computer or on multiple computers that are locatedat one site or distributed across multiple sites and interconnected by acommunication network.

These functions described above can be implemented in digital electroniccircuitry, in computer software, firmware or hardware. The techniquescan be implemented using one or more computer program products.Programmable processors and computers can be included in or packaged asmobile devices. The processes and logic flows can be performed by one ormore programmable processors and by one or more programmable logiccircuitry. General and special purpose computing devices and storagedevices can be interconnected through communication networks.

Some implementations include electronic components, for examplemicroprocessors, storage and memory that store computer programinstructions in a machine-readable or computer-readable medium(alternatively referred to as computer-readable storage media,machine-readable media, or machine-readable storage media). Someexamples of such computer-readable media include RAM, ROM, read-onlycompact discs (CD-ROM), recordable compact discs (CD-R), rewritablecompact discs (CD-RW), read-only digital versatile discs (e.g., DVD-ROM,dual-layer DVD-ROM), a variety of recordable/rewritable DVDs (e.g.,DVD-RAM, DVD-RW, DVD+RW, etc.), flash memory (e.g., SD cards, mini-SDcards, micro-SD cards, etc.), magnetic or solid state hard drives,read-only and recordable Blu-Ray® discs, ultra density optical discs,any other optical or magnetic media, and floppy disks. Thecomputer-readable media can store a computer program that is executableby at least one processing unit and includes sets of instructions forperforming various operations. Examples of computer programs or computercode include machine code, for example is produced by a compiler, andfiles including higher-level code that are executed by a computer, anelectronic component, or a microprocessor using an interpreter.

While the above discussion primarily refers to microprocessor ormulti-core processors that execute software, some implementations areperformed by one or more integrated circuits, for example applicationspecific integrated circuits (ASICs) or field programmable gate arrays(FPGAs). In some implementations, such integrated circuits executeinstructions that are stored on the circuit itself.

Furthermore, it is understood that any specific order or hierarchy ofsteps in the processes disclosed is an illustration of exampleapproaches. Based upon design preferences, it is understood that thespecific order or hierarchy of steps in the processes may be rearranged,or that all illustrated steps be performed. Some of the steps may beperformed simultaneously.

The various embodiments described above are provided by way ofillustration only and should not be construed to limit the scope of thedisclosure. Those skilled in the art will readily recognize variousmodifications and changes that may be made to the principles describedherein without following the example embodiments and applicationsillustrated and described herein, and without departing from the spiritand scope of the disclosure.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a sub combination.

CONCLUSION

A system and method has been shown in the above embodiments for theeffective implementation of tube transportation systems using a gaseousmixture of air and helium. While various preferred embodiments have beenshown and described, it will be understood that there is no intent tolimit the invention by such disclosure, but rather, it is intended tocover all modifications and alternate constructions falling within thespirit and scope of the invention, as defined in the appended claims.

The invention claimed is:
 1. An article of manufacture havingnon-transitory computer readable storage medium comprising computerreadable program code executable by a processor to implement a method todetermine optimum operating points for power/cost and helium-air ratiosin a plurality of substantially evacuated tubes in a tubulartransportation system for transporting one or more passengers or one ormore cargos via a capsule along a predetermined route, thenon-transitory computer readable storage medium comprising: (a) computerreadable program code identifying a speed of the capsule; and (b)computer readable program code identifying a pressure to be maintainedwithin a tube amongst the plurality of substantially evacuated tubes;(c) computer readable program code identifying, for the speed identifiedin (a), a helium-air ratio based on an analysis of a total powerrequired at a plurality of percentages of helium for the pressureidentified in (b); (d) computer readable program code sendinginstructions to maintain within the tube amongst the plurality ofsubstantially evacuated tubes, a percentage of helium according to thehelium-air ratio identified in (c).
 2. The article of manufacture ofclaim 1, wherein the pressure identified in (b) is picked from thefollowing range: 1 Pa to 1000 Pa.
 3. The article of manufacture of claim1, wherein each of the plurality of percentages of helium in (c) arepicked from the following range: 50% to 99%.
 4. The article ofmanufacture of claim 1, wherein the speed of the capsule identified in(a) has a value that is within the following range: 600 km/hr to 1100km/hr.
 5. The article of manufacture of claim 1, wherein the total powerin (c) is a function of a first power to pump each tube to thesubstantially evacuated state and a second power to overcome aerodynamicdrag.
 6. The article of manufacture of claim 5, wherein thenon-transitory computer readable storage medium further comprises:computer readable program code computing, for each of the plurality ofpercentages of helium in (c), a first power required to maintain thetube amongst the plurality of substantially evacuated tubes at thepressure identified in (b) and a second power corresponding to thecapsule to overcome aerodynamic drag; and computer readable program codecomputing, for each of the plurality of percentages of helium in (c), asum of the first power and the second power to determine the total powerin (c).
 7. The article of manufacture of claim 5, wherein thenon-transitory computer readable storage medium further comprises:computer readable program code accessing a first dataset of the firstpower versus the plurality of percentages of helium; computer readableprogram code accessing a second dataset of second power to overcomeaerodynamic drag versus the plurality of percentages of helium; computerreadable program code computing a third dataset of the total powerversus the plurality of percentages of helium wherein, for each of theplurality of percentages of helium, a sum of the first power from thefirst dataset and the second power from the second dataset is used todetermine the total power.
 8. The article of manufacture of claim 7,wherein the first dataset and second dataset are accessed by looking upat least one look-up table.
 9. The article of manufacture of claim 1,wherein the analysis in (c) is based on any of the following powervalues: affordable power, minimum power, or acceptable power.
 10. Anarticle of manufacture having non-transitory computer readable storagemedium comprising computer readable program code executable by aprocessor to implement a method to determine optimum operating pointsfor power/cost and helium-air ratios in a plurality of substantiallyevacuated tubes in a tubular transportation system for transporting oneor more passengers or one or more cargos via a capsule along apredetermined route, the non-transitory computer readable storage mediumcomprising: (a) computer readable program code identifying a speed ofthe capsule; (b) computer readable program code identifying a pressureto be maintained within a tube amongst the plurality of substantiallyevacuated tubes; (c) computer readable program code identifying, foreach of a plurality of percentages of helium, a first power required tomaintain the tube amongst the plurality of substantially evacuated tubesat the pressure identified in (b) and a second power corresponding tothe capsule to overcome aerodynamic drag; (d) computer readable programcode computing, for each of the plurality of percentages of helium in(c), a sum of the first power and the second power to determine a totalpower for the speed identified in (a); (e) computer readable programcode identifying a helium-air ratio from an optimal value within totalpower values computed in (d) for the speed identified in (a); and (f)computer readable program code sending instructions to maintain withinthe tube amongst the plurality of substantially evacuated tubes, apercentage of helium according to the helium-air ratio identified in(e).
 11. The article of manufacture of claim 10, wherein the pressureidentified in (b) is picked from the following range: 1 Pa to 1000 Pa.12. The article of manufacture of claim 10, wherein each of theplurality of percentages of helium in (c) are picked from the followingrange: 50% to 99%.
 13. The article of manufacture of claim 10, whereinthe speed of the capsule identified in (a) has a value that is withinthe following range: 600 km/hr to 1100 km/hr.
 14. The article ofmanufacture of claim 10, wherein the optimal value in (e) is based onany of the following power values: affordable power, minimum power, oracceptable power.
 15. An article of manufacture having non-transitorycomputer readable storage medium comprising computer readable programcode executable by a processor to implement a method to determineoptimum operating points for power/cost and helium-air ratios in aplurality of substantially evacuated tubes in a tubular transportationsystem for transporting one or more passengers or one or more cargos viaa capsule along a predetermined route, the non-transitory computerreadable storage medium comprising: (a) computer readable program codeidentifying a speed of the capsule; (b) computer readable program codeidentifying a pressure to be maintained within a tube amongst theplurality of substantially evacuated tubes; (c) computer readableprogram code accessing a first dataset of a first power versus aplurality of percentages of helium, the first power required to maintainthe tube amongst the plurality of substantially evacuated tubes at thepressure identified in (b); (d) computer readable program code accessinga second dataset of a second power to overcome aerodynamic drag versusthe plurality of percentages of helium; (e) computer readable programcode computing a third dataset of the total power versus the pluralityof percentages of helium wherein, for each of the plurality ofpercentages of helium, a sum of the first power from the first datasetand the second power from the second dataset is used to determine thetotal power; (f) computer readable program code identifying a helium-airratio from an optimal value within total power values computed in (e)for the speed identified in (a); and (g) computer readable program codesending instructions to maintain within the tube amongst the pluralityof substantially evacuated tubes, a percentage of helium according tothe helium-air ratio identified in (f).
 16. The article of manufactureof claim 15, wherein the pressure identified in (b) is picked from thefollowing range: 1 Pa to 1000 Pa.
 17. The article of manufacture ofclaim 15, wherein each of the plurality of percentages of helium in (c)are picked from the following range: 50% to 99%.
 18. The article ofmanufacture of claim 15, wherein the speed of the capsule identified in(a) has a value that is within the following range: 600 km/hr to 1100km/hr.
 19. The article of manufacture of claim 15, wherein the optimalvalue in (f) is based on any of the following power values: affordablepower, minimum power, or acceptable power.
 20. The article ofmanufacture of claim 15, wherein the first dataset and second datasetare accessed by looking up at least one look-up table.